Response parameters that control the service, safety and collapse performances of a 253 m tall concrete core wall building in Istanbul

Seismic performance of a 253 m tall reinforced concrete core wall building constructed in Istanbul, designed according to performance-based seismic design principles, is assessed for determining the response parameters that control the serviceability, safety and collapse performance limit states. Serviceability performance is evaluated under the 50-year wind and 43-year earthquake whereas safety performance is assessed under the 2475-year earthquake. Collapse performance is elaborated through incremental dynamic analysis. Our study revealed that the service performance is controlled by the maximum interstory drift limits specified for wind loads, and safety performance is controlled by the flexural steel strain limits of coupling beams. Collapse occurs in two consecutive stages: flexural collapse of coupling beams, followed by crushing of concrete at critical shear wall segments. Collapse spectra are defined for these two collapse limit states. Collapse spectra can be extrapolated from the 2475-year maximum considered earthquake spectrum provided that the prevailing inelastic mechanisms are similar under the MCE and collapse ground motions. The building displays a significantly higher seismic performance at all performance levels, which is primarily attributed to the overstrength due to the limitation of axial stresses on vertical members under design earthquake load combination. The annual frequency of the mean earthquake ground motion that leads to incipient collapse is determined as 8·10−5, which is significantly lower than the annual frequency of 2475-year ground motions.


Introduction
The population of tall buildings, with a significant portion in regions of high seismicity, is steadily increasing in the world. Design of tall buildings under gravity and wind loading in non-seismic regions is well developed and has a history longer than a century. However, tall building boom in seismic regions is a new phenomenon. In Istanbul, the number of buildings taller than 100 m has exceeded 200 (Erdik et al. 2003;Odabasi et al. 2021). Tall buildings are unique in architectural and structural features when compared to ordinary multistory buildings. These differences become more prominent in seismic zones where seismicity and unique dynamic building characteristics dominate structural design. Past seismic design practices and existing prescriptive procedures may not promote the desired behavior for tall buildings under earthquake excitations (Moehle 2008;Brunesi et al. 2016;Mazzotta et al. 2017;Beiraghi and Siahpolo 2017). Hence, chapters devoted particularly to tall buildings are included in the recent seismic design codes, or pertinent guidelines have been published (AFAD 2018a;LATBSDC 2017;PEER 2017;SEAONC 2007;MHUD-PRC 2010).
There are three critical issues in the design of tall buildings in seismic regions. First, seismic codes and guidelines for regulating tall building design have been developed fairly recently and they are mostly informative, not yet legally binding in all countries. Second, tall buildings are not typical in their structural systems. There is even no consensus on the description of a tall building. Design engineers are developing new forms by utilizing new member types and materials for attaining further increased heights. Third, existing tall buildings in seismic regions have not yet experienced strong ground shaking at design level seismic intensities. Hence, there is no reliable field data on the damages and losses sustained by tall buildings under strong earthquakes as well as the economical and psychological impact of these losses on societies.
Most of the studies on the seismic performance of tall buildings are carried out on rigorous analytical models of "case study" buildings with the objective of estimating probable risks and consequent losses. In fact, each tall building, either constructed or only designed, is indeed a particular case. The uncertainty in ground motions dominated the overall uncertainty in probabilistic seismic demand analyses where the uncertainties in material properties were incorporated in the finite element model. Hence, ground motions were the only source of uncertainty taken into account in the development of fragility curves. Lu et al. (2013) carried out the collapse simulation of a 550 m tall, 119-story mega-braced framecore tube building (to be built) in China by developing a rigorous nonlinear finite element model. Their simulation revealed that the main collapse mode of this structural system, which is common in regions of high seismicity, is of vertical "pancake" type. In addition, the collapse regions do not necessarily coincide with the initial plastic zones under maximum considered earthquake (MCE) ground motions. Shome et al. (2015) analyzed two 42-story tall RC buildings with a dual system and a core wall system, and a 40-story buckling-restrained braced steel building that were designed using various design standards and guidelines, under a variety of earthquake ground motions. The objective was estimating the mean monetary loss and its uncertainty based on the PEER performance-based earthquake engineering methodology (PEER 2010). The dual-system building was found to perform better than the other building systems. Alwaeli et al. (2017) developed seismic scenario based building specific performance limit state criteria, in terms of net interstory drift due to shear and flexural deformations, for tall RC wall buildings using a 30-story RC wall building as a case study. They showed that the performance limit states are dependent on the structural system, arrangement and geometry of vertical elements and axial force level in the lower stories. Zhang and He (2020) carried out seismic collapse risk assessment of a 660 m tall, 118-story building with a typical mega-frame/core-tube/outrigger resisting system. Fragility curves incorporating the uncertainties in material and damping properties were developed, by employing stripe analysis. Peak ground displacement when used as the seismic intensity measure as opposed to peak ground acceleration and peak ground velocity in developing the fragility curves, the overall uncertainty was significantly reduced. However, the uncertainty in ground motions due to the record-to-record variability was significant consistent with previous studies.
Research studies on constructed tall buildings aiming at determining the relations between the adopted seismic design criteria and the achieved seismic performances are limited in literature (Korista et al. 1997;Fan et al. 2009;Wang et al. 2017;Bilotta et al. 2018). The presented study aims at closing this gap, by investigating and identifying the critical structure-specific or member-specific response parameters that significantly control the serviceability, safety and collapse performances of a 253 m tall skew plan concrete core wall building, which was recently constructed in Istanbul. Seismic design of this building was based on state-of-the-art guidelines and practices prevailing during the planning stage of the project in 2016 (Budak et al. 2018). It is expected that the findings of this study may further improve the understanding of the seismic performance of tall concrete core wall buildings designed by professional practitioners under strong earthquake excitations. Along this perspective, determining the crucial response characteristics that dominate the limit states, the inherent sources of overstrength, and the intensities and annual occurrence frequencies of earthquake ground motions leading to local and global collapse are introduced as the key aspects of tall building design.

Building characteristics
The building is a 253 m tall, 62-story reinforced concrete building, including eight podium floors below the ground level, the ground (G) floor and 53 floors above the ground level. Typical floor-to-floor height is 4.0 m, whereas the height of the ground story is 8.75 m and the total height of the podium stories is 31.75 m. The building was designed for office use. Figure 1 shows building section, typical podium floor plan and the view of the building from the northeast corner during its construction. The parallelogram footprint was necessitated due to the plan optimization based on the available land geometry, which causes additional torsional effects under lateral loading.
Typical floor plan of the tower is shown in Fig. 2. The thickness of the main segments of the core shear walls at the lower stories are 1.00 m for P1-P8 and 1.10 m for P22 and P25. Thicknesses gradually reduce in four stages to 0.60 m at the upper stories. P24 is 0.  There are two types of coupling beams at each story. One type is 2.2 m long and 0.85 m deep, and the other type is 3.3 m long and 1.12 m deep. The clear span to depth ratios are 2.6 and 2.9, respectively. Their thicknesses conform to the thickness of adjacent walls.
The building has a 4.8 m thick mat foundation under the tower, which gradually reduces to 3.5 m, 2.0 m and 1.5 m under the podium floors. It is located on stiff soil (Soil Group ZC; MPWS 2007), equivalent to NEHRP Type C (FEMA 2020), where the average shear wave velocity in the upper 30 m of the site profile, V s30 , is 500 m/s.
Concrete characteristic strength, f ck , is 60 MPa at the core walls, coupling beams and tower columns, and 40 MPa at all other members. Characteristic yield strength of reinforcing steel, f yk , is 420 MPa whereas yield strength of structural steel, f y , in composite members is 460 MPa.

Structural design
Structural design was completed in 2016. Hence, seismic codes and standards prior to 2016 were considered in design. The structural system of the tower is composed of a core wall connected to peripheral columns and beams with flat plates. Wind tunnel tests were carried out in order to determine the design wind load distributions (ASCE 2012;WTG 1996;CEN 2005).
Two different performance targets were considered in seismic design (SEAONC 2007;PEER 2010): operational performance under an earthquake with a return period of 43 years (service-level earthquake; SLE) and collapse prevention performance under 2475-year earthquake (MCE) ground motions. Structural design and detailing was based on response spectrum analysis under the SLE. Capacity shears were employed in the shear design of ductile members. The dominant design load combination that includes seismic action for the SLE is where D is the dead load, L is the live load and E h is the horizontal design earthquake load ( E h = ±E X ± 0.3E Y ); E X and E Y are the earthquake actions obtained from response spectrum analysis along the X and Y directions, respectively. The design approach with pertinent limitations imposed are summarized in the following.

Axial load limits
Maximum permitted normalized compressive stresses acting on RC members are N d ∕A c f ck < 0.40 for concrete columns and N d ∕A c f ck < 0.25 for shear walls, where N d is the axial load demand calculated under the design load combination in Eq. (1) and A c is the gross area of the concrete cross section. For composite columns, the maximum value of the axial load is N d < 0.4N ro when N d is calculated from the 1.2D + L + E h load combination (MPWS 2007), and N d < 0.8N r when N d is calculated from the 1.4D + 1.6L combination (TSI 2000), where N ro and N r are the axial load capacities of the composite columns: where A co is the net concrete area, A s is the longitudinal reinforcement area and A a is the area of the steel section.

Reinforcement limitations
Limitations on reinforcement were dictated by the existing design codes (MPWS 2007;TSI 2000;ACI 2014). Longitudinal reinforcement ratio for RC columns is 0.01 < < 0.04 . For composite columns, the area of the steel section should exceed s = 0.04 times the gross section area. In the web region of shear walls, > 0.0025 of the web cross-sectional area whereas in the confined end regions of shear walls, > 0.0020 of the total wall area within the critical height region and > 0.0010 above the critical height region. For beams, the longitudinal tensile reinforcement ratio should satisfy 0.6f ctk ∕f yk < < 0.02 as well as < 0.85 b . Here, f ctk is the characteristic tensile strength of concrete and b is the balanced tensile reinforcement ratio. Further detailing requirements are not repeated here as they are common in the existing design codes.

Flexural design
Design bending moments for columns, core walls and beams were determined from the response spectrum analysis under the load combination in Eq. (1). Design bending moment distributions for the core walls were modified to consider dynamic amplification (Moehle et al. 2012), in order to ensure that plastic hinging only occurs at the designated critical sections of the walls. Critical wall sections in this building where maximum bending moments develop are at the base of the ground story and above the podium floor. (2)

Shear design
Design shear forces for beams and columns are the capacity shear forces, which are based on the flexural strength of the end sections. Design shear forces in core walls at any section were calculated from where M p,t is the moment capacity at the critical section of the core wall, and M d,t is the bending moment and V d is the shear force calculated at the critical section under the SLE. However, these forces should not exceed 3.5V d . Critical wall height is 1/6 of the total wall height above the critical section (MPWS 2007).

Performance limits under the SLE and wind
Column, beam and core wall moment demand-to-capacity ratios (DCRs) for deformation controlled actions should not exceed 1.5 under the design load combination given in Eq. (1). Similarly, shear DCRs of these members should not exceed 0.7 in order to suppress the shear mode of failure. Expected material strengths were employed for calculating the capacities, which are 1.3f ck , 1.17f yk and 1.1f y for concrete, reinforcing steel and structural steel, respectively (LATBSDC 2017).
Interstory drift ratio (IDR) is limited to 0.5% under the SLE (PEER 2010; LATBSDC 2017) for ensuring that the system remains essentially linear elastic. Furthermore, IDR is limited to 1/500 (0.2%) under 50-year wind load (Smith 2011;Arup Inc. 2013). Performance of the building is deemed satisfactory if the calculated compressive strains for confined concrete are less than 0.010 and reinforcing steel tensile strains are less than 0.030 for columns, core wall segments, beams and coupling beams (PEER 2010).

Analytical models
3-D linear elastic and inelastic finite element models of the building were developed for calculating the design forces and deformations under the SLE and MCE excitations, respectively.

Linear elastic finite element model
Linear elastic model of the building was developed for response spectrum analysis under the load combination in Eq. (1) by using the ETABS software (CSI 2011), as well as static analysis under equivalent static wind loads. Shell elements were employed for the shear walls and slab members whereas the column and beam members were represented by frame elements. Gross section properties were reduced by effective section stiffness multipliers for the SLE and wind loading: 0.90 for columns, 0.75 for shear walls, 0.70 for perimeter beams, 0.50 for slabs and 0.30 for coupling beams (PEER 2010).
An eigenvalue analysis of the linear elastic structural model was performed. Table 1 provides the natural vibration periods and effective modal masses for the first six vibration modes. Rotation is apparently dominant in the third and fifth modes. Mode shapes for the first three modes are presented in Fig. 3. The amplitudes of rotation components θ are scaled for a fair comparison. The first two modes are translation dominant along two orthogonal oblique axes due to the parallelogram layout of the structural system on plan whereas the third mode is rotation dominant. The centrally located core wall in this building provides not only lateral but also torsional resistance since the torsional stiffness of the core wall is large due to fairly long moment arm between the coupling wall segments. Hence, the system is torsionally stiff as confirmed by the ordering of the modal periods.

Inelastic finite element model
The 3-D inelastic dynamic model was further developed for nonlinear analysis under the MCE and collapse ground motions using the Perform3D software (CSI 2016). Fiber-type shell elements were used for shear walls, and lumped plasticity models were employed for frame members responding beyond the linear elastic range (PEER 2010;Wallace 2007;Zekioglu et al. 2007).
Previous studies show that the use of typical concrete material models (e.g., Mander et al. 1988) in modeling shear walls lead to inaccurate simulation of cyclic responses  (Pugh et al. 2015;Lowes et al. 2016). Hence, regularized concrete material response, modifying post peak stress-strain response based on concrete fracture energy, developed by these researchers, was used for the fiber-type shell elements in order to capture the cyclic responses and drift capacities accurately. Steel bars in tension were represented by the elasto-plastic steel model with 1% strain hardening, whereas steel bars in compression were represented by the simple buckling steel model proposed by Pugh et al. (2015) for simulating the wall response until concrete reaches residual compressive strength.
Stress-strain relations for concrete in compression and steel in tension are presented in Fig. 4. Quasi-elastic frame elements were employed for the column and beam members responding in the linear elastic range. These are the middle segments of beams and columns between the plastic hinges defined at the member ends. They do not undergo inelastic flexural response. Effective section stiffness multipliers were 0.70 for columns, 0.35 for perimeter beams, 0.50 for slabs and 0.20 for coupling beams (LATBSDC 2017). These values are larger compared to the stiffness multipliers employed for linear elastic members under SLE ground motions given in Sect. 4.1. Although inelastic actions do not develop in these members due to capacity design under both the SLE and MCE excitations, more cracking is expected, hence larger stiffness reduction is required under the MCE ground motions due to larger end moments transferred from the plastic hinges at member ends that attain their yield capacities.
For inelastic response properties of perimeter and coupling beams, piecewise linear moment-curvature relationships were defined along the plastic hinge lengths. The lengths of plastic hinges were assumed as one-half of the cross-section depth, at both ends of all beam elements (Park and Paulay 1975). Moment-curvature relations were derived for the plastic hinges by using the Mander model (Mander et al. 1988) for unconfined and confined concrete, and the elasto-plastic model shown in Fig. 4b for steel.
Column elements were modeled with P-M-M hinges. Geometric nonlinearity was also taken into account in the 3-D analytical model. Slab members in the nonlinear model were idealized as equivalent beam type elements per ASCE 41-13 (ASCE 2014). The diagonal outrigger members are tension-compression members; hence, their nonlinear response was represented by a nonlinear concrete strut in compression and by an elasto-plastic steel bar with 1% strain hardening in tension.

Probabilistic seismic hazard analysis and strong ground motions
A site-specific probabilistic seismic hazard analysis (PSHA) was performed to develop the response spectra for hazard levels of 50% probability of exceedance (PE) in 30 years and 2% PE in 50 years, which respectively correspond to mean recurrence intervals of 43 and 2475 years, i.e. the SLE and MCE. The PSHA methodology relies on the historical and recorded seismicity as well as neotectonic faulting structure of the Istanbul region and ground motion modeling (Akkar 2014). Figure 5a presents the 2.5% and 5% damped site-specific acceleration response spectra for the SLE and MCE hazard levels, respectively. Viscous damping ratio, , is taken as 2.5% rather than the conventional 5% in obtaining the SLE spectrum, because very limited concrete cracking is expected under the SLE excitation (PEER 2017). The MCE spectrum is employed as target spectrum in selecting and scaling the 18 MCE ground motion pairs (Akkar 2014). Acceleration spectra rather than the displacement spectra is employed for scaling of ground motions since the MCE spectrum is expressed as a uniform hazard acceleration response spectrum in seismic codes and seismic hazard maps, obtained through conventional probabilistic seismic hazard analysis. When the displacement spectrum is available as in Eurocode 8 (CEN 2004), ground motions can be scaled to the target MCE displacement spectrum with similar efficiency (Brunesi et al. 2016).
Deaggregation for the MCE hazard yielded the earthquakes that contribute most significantly as moment magnitude ( M w ) 7.5 earthquakes occurring at epicentral distances ( R JB ) 26-49 km. Accordingly, the strong ground motion records were selected from the PEER NGA Database (PEER 2022) with the following constraints pertaining to the construction site: 6.0 ≤ M w ≤ 8.0 , R JB ≤ 50km , and 300m∕s ≤ V s30 ≤ 700m∕s . Then, ground motion amplitude scaling was carried out on the geometric mean spectrum of each pair according to the ASCE 7-16 (ASCE 2017) procedure. The seismological properties and scale factors (SFs) of the ground motions are given in Table 2. Figure 5b presents the response spectra of these near fault ground motions that were scaled to match the target MCE spectrum.
Selection and scaling of ground motions were conducted according to the ASCE 7-16 procedure as mentioned above. The main reason for utilizing this procedure is its wide acceptability and availability in most seismic design codes. However, recent studies indicate that although this procedure is accurate, it is not necessarily efficient (Eren et al. 2021). Zhang et al. (2018) introduced a spectral-velocity-based ground motion intensity measure Fig. 5 a Site-specific SLE and MCE response spectra and b acceleration response spectra of ground motions scaled to MCE response spectrum calculated at multiple modal periods for tall buildings that leads to higher efficiency, i.e., less dispersion of maximum IDRs under the ground motions scaled with respect to this intensity measure.

Response parameters that control the service performance level under SLE
The target performance level for tall buildings under the SLE and 50-year wind is "operational." Hence, the response should be essentially linear elastic. This is ensured by the performance limits stated in Sect. 3.5, in terms of IDRs and structural member DCRs. IDRs throughout the building height are shown in Fig. 6a, under the SLE spectrum and the 50-year wind forces in both directions. Significant higher mode effects can be observed in the more flexible X-direction particularly below the outrigger level both under the SLE and 50-year wind. Wind forces control interstory drifts up to floor 30 (below the outrigger level) and the earthquake forces control drifts above floor 30. However, IDRs are significantly below the 0.5% limit under the SLE, and reasonably below the 0.2% limit under the 50-year wind.
Moment and shear DCRs of selected shear wall segments are presented in Fig. 7. All DCR values are well below the moment DCR limit of 1.5 and the shear DCR limit of 0.7. Respective DCR values for the peripheral columns are much lower, maximum moment DCRs around 0.6 and shear DCRs around 0.2.
A comparative graphical view of the maximum DCRs for each member type and maximum IDRs throughout the building height is presented in Fig. 8 in a normalized form. The  The response parameter that controls the service performance level of this building is apparently the maximum IDR under the 50-year wind. On the other hand, in seismic regions with very low wind speeds, the service performance of a core wall building would be controlled by the moment and shear DCRs of the coupling beams.
Outriggers were employed in the investigated structural system mainly for reducing the IDRs under wind loads. However, the results displayed in Fig. 6b indicate that this reduction is not significant. The 0.2% IDR limit for 50-year wind would have been satisfied without outriggers. This is perhaps due to the competent lateral stiffness of the core wall system, which is an outcome of imposing the stress limits indicated in Sect. 3.1. The role of outriggers might have been more prominent in the reduction of floor accelerations for comfort, but such a criterion is not imposed in tall building design (Smith 2011).
The maximum IDRs under the SLE are significantly lower than the IDR limits for service performance (Figs. 6a and 8). Hence, imposing limits on IDRs is not effective at the service performance level of a tall concrete core wall system. IDR limits may be more effective on tall steel buildings.

Response parameters that control the safety performance level under MCE
The target performance level under the MCE is "collapse prevention." Hence, seismic response under the MCE ground motions is expected to be inelastic. This target performance is satisfied if the performance limits stated in Sect. 3.6, in terms of IDRs and material strains of structural members, are not exceeded. Nonlinear time history analyses (NTHA) were conducted under the 18 pairs of ground motions scaled to the MCE spectrum. Damping matrix was constructed by using 2.5% Rayleigh damping ratios for the first and fifth modes. 2.5% rather than the conventional 5% damping was preferred in the NTHA because damping matrix represents energy dissipation in linear elastic members whereas hysteretic energy dissipation is inherently accounted by the inelastic member responses. Figure 9 presents the normalized mean material strains in the most critical members and normalized IDRs at the most critical story under the MCE ground motion pairs. Mean concrete and steel strains, c and s , are normalized with the MCE limits of c,MCE = 0.010 and s,MCE = 0.030, respectively, whereas mean IDRs are normalized with 3.0%. It is worth noticing that the limiting concrete strain is equal to the ultimate strain calculated for the regularized concrete model given in Fig. 4. Figure 10 presents the normalized concrete and steel strains in shear wall segments determined under each MCE ground motion pair. Likewise, maximum IDRs can be seen in Fig. 11, which shows the variation of maximum base shear forces (normalized with the building weight) against maximum IDRs in each direction, calculated under the SLE spectrum and MCE ground motions. Note that maximum base shear and IDR are not necessarily synchronous.
The normalized mean material strains in shear wall segments shown in Fig. 10 and IDRs in Fig. 11 under the 18 MCE ground motion pairs are quite low compared to the respective MCE limits. Shear walls are effectively at the incipient yielding state, whereas the coupling beams are purely in the yielding phase during their maximum responses under the MCE ground motions, as marked on the moment-curvature diagrams of the most critical 1 3 members in Fig. 12. NTHA also indicate that the peripheral columns remain linear elastic under the MCE ground motions. Therefore, Figs. 9, 10 and 12 reveal that the safety performance level under the MCE is dominantly controlled by the tensile steel strains, and hence by the plastic curvatures of coupling beams. The mean tensile strain in the coupling beams is the product of normalized steel strain in coupling beams (0.72) from Fig. 9 and the MCE limit for steel, s,MCE = 0.030, which gives 0.022. This mean strain is about 10 times of the yield strain of S420 steel, i.e., 0.0021, which confirms that coupling beams are in the far inelastic stage under the MCE ground motions as clearly indicated in Fig. 12b.

Response parameters that control the collapse performance
Each ground motion pair is scaled upwards from the MCE level by incrementally increasing their geometric mean spectrum until collapse is achieved. Collapse occurs in two consecutive stages. In the first stage, a coupling beam fails when maximum curvature exceeds the ultimate curvature of the beam (e.g., 0.122/m for CB2 on floor 14; see Fig. 12b). Concrete and steel strains in shear walls are far from critical at this stage, as shown in Fig. 13. Note that concrete and steel strains are now normalized with the ultimate limits, cu = 0.010 and su = 0.080, respectively. As upward scaling continues incrementally, almost all coupling beams fail before the commencement of concrete crushing at the critical shear wall fibers. The computer algorithm permits further analysis steps with zero stiffness and strength of the failed coupling beams. In the second stage, failure occurs when concrete strain at the most critical shear wall reaches the crushing strain of 0.01. Figure 14 shows the normalized concrete and steel strains in shear wall segments at this stage under each ground motion pair.
These two failure stages, identified with the first coupling beam failure and the first shear wall concrete crushing in Figs. 13 and 14, are defined as partial collapse and near collapse, respectively. The response parameters that control these two collapse stages are the coupling beam ultimate curvatures (Fig. 12b) or their corresponding tensile steel strains, and shear wall compressive concrete strains (Fig. 14a). The increase in concrete and steel strains from partial to near collapse states are clearly observed comparatively in Figs. 13 and 14. Under each ground motion, the wall segment that reaches concrete crushing earliest controls ultimate failure. P1, P3 and P7 are the most controlling shear wall segments (see Fig. 2). Along each vertical ground motion line in Fig. 14, as the critical wall segment approaches crushing along the degrading stress-strain segment in Fig. 4a, the other wall segments do not follow the critical one closely, which can be attributed to the redistribution of internal stresses in the core wall. Figure 15 presents the geometric mean acceleration response spectra of the ground motion pairs scaled to the first coupling beam failure (partial collapse) and the first shear wall failure (near collapse) stages. Their mean spectra are identified as the partial collapse spectrum (PCS) and near collapse spectrum (NCS). Together with the mean spectrum of ground motions scaled to the MCE spectrum, they are compared in Fig. 16a with the site specific uniform hazard spectra, which are standardized to the code spectrum format for return periods of 43, 475 and 2475 years (i.e., the SLE, the design basis earthquake DBE and the MCE, respectively).

Prediction of partial collapse spectrum from the MCE spectrum
Seismic codes and regulations for tall building design mandate NTHA under selected ground motion pairs scaled to the MCE spectrum. For the investigated tall concrete building, the moment-curvature response for the most critical coupling beam under each MCEscaled ground motion pair is readily available, as indicated in Fig. 12b. Under the MCE ground motions, maximum curvatures are all located on the post-elastic linear segment of the moment-curvature diagram. As the intensity of each ground motion is incrementally increased, the associated curvature point moves away from the MCE point on the postelastic linear segment until it reaches the ultimate curvature capacity of the coupling beam. The inelastic mechanism of the building does not change between these two limit states, i.e., the critical coupling beam and all others are in the post-elastic "segmental linear" state ( Fig. 12b) while the shear wall members are at the incipient inelastic response state (Fig. 12a). This stable segmental linearity from MCE to partial collapse under each ground motion for the most critical coupling beam, i.e., the one that reaches the failure state first, motivates searching for the similarity of the ratio of ground motion scale factors and the ratio of absorbed plastic energies between the MCE and ultimate curvature states.
The ratio of PCS to MCE spectrum, both given in Fig. 16b, is very stable along the period axis, with a mean value of 2.35 and almost with no dispersion. The ratio of absorbed plastic energies under the post-elastic linear moment-curvature segment in Fig. 12b for a unit plastic hinge length, from yield to the MCE curvature and from yield to the end of the linear post-elastic segment, i.e., 0.122/m at incipient collapse, can be calculated for each ground motion. Their mean value is 2.48, which is sufficiently close to the spectrum scale factor 2.35 with a mere 5% difference. Consequently, if the MCE spectrum is scaled Fig. 16 a Mean acceleration response spectra of MCE ground motions, partial collapse and near collapse spectra, and the standardized code spectra for 43, 475 and 2475 year return periods b comparison of the PCS with the scaled MCE spectrum by 2.48, the PCS can be closely estimated without carrying out an onerous incremental dynamic analysis for each ground motion. This is a significant economical saving in estimating collapse. The estimated PCS is displayed in Fig. 16b and compared with the actual PCS.
It should be noted that a similar scaling cannot be applied to the MCE spectrum for obtaining the NCS, because the inelastic mechanism of the building changes significantly between the partial collapse state (coupling beam collapse) and the near collapse state (shear wall collapse). Figure 17 shows the seismic hazard curve in terms of spectral acceleration at the fundamental period of the building, T 1 , that is constructed (Cornell et al. 2002) using the available hazard data for the building site (41.0812°N, 29.0096°E; Soil Group ZC; AFAD 2018b), which include hazard levels with mean recurrence intervals, T r = 43, 72, 475 and 2475 years. Mean spectral acceleration values at T 1 for the ground motions that will lead to partial and near collapse of the building, i.e., 0.21 g and 0.31 g, respectively, cf. Figure 15, are entered into the constructed hazard curve. The return periods of the mean partial and near collapse ground motions are estimated as 12,000 and 27,000 years, respectively.

Discussion and conclusions
The investigated tall RC core wall building, designed according to performance-based design principles as outlined, displays remarkable seismic performance. It remains linear elastic under the SLE, and displays limited damage performance under the MCE ground motions. Significant inelastic actions occur only at the coupling beams and particular sections of the core walls where ductile flexural response is ensured.
Service performance level is either controlled by the force response of coupling beams expressed in terms of DCR limits in the regions of low wind speeds, or maximum IDR limits specified for wind loads in the regions of high wind speeds. Safety and partial collapse limit states are controlled by the flexural response limits of coupling beams whereas near collapse limit state is controlled by the concrete strain limits at the confined shear wall end The basic reason behind such favorable seismic performance is the overstrength in design, primarily due to the limitation of axial forces in vertical members. The outrigger trusses employed for deformation control under wind loading also contribute to overstrength, although to a lesser extent. An overstrength ratio can be defined in both directions, as the maximum ratio of the MCE to SLE base shear demands from Fig. 11. These are 5.8 and 4.6 in the X and Y directions, respectively. Both factors are about twice the overstrength factors suggested in ASCE 7-16 (ASCE 2017) for ordinary concrete buildings. Substantial overstrength and its associated benefits were also observed in the 508 m tall Taipei 101 tower (Fan et al. 2009).
The inherent overstrength in seismic design reduces the damage risk and increases the seismic performance significantly. The annual frequency of the mean earthquake ground motion that will lead to collapse reduces from the target value of 4·10 −4 (1/2475) defined for the MCE for ordinary buildings, to 8·10 −5 (1/12000) for partial collapse, and to 4·10 −5 (1/27000) for near collapse of the tall core wall building. However, this safety increase cannot be regarded as a waste of resources. It comes at a cost that can be considered negligible when compared to the large investment cost of a tall building. It has to be considered that tall buildings, which are designed to meet the current performance based guidelines, have not yet been tested under extreme earthquake ground motions.
A modest contribution of this study is the direct estimation of ground motions leading to partial collapse from the MCE ground motions through a simple scaling procedure introduced herein for tall RC buildings. The primary lateral load resisting system of tall RC buildings is a core wall composed of wall segments connected with coupling beams. The introduced procedure utilizes the segmental linearity of the moment-curvature response of coupling beams along the post-yield branch. As the intensity of ground motions increase during incremental dynamic analysis, plastic curvatures of coupling beam plastic hinges increase linearly from the MCE level to the upward-scaled intensity of the MCE ground motion until the collapse of the most critical coupling beam occurs (partial collapse state). Accordingly, the scale factor for each ground motion leading to partial collapse can be obtained as the ratio of the absorbed plastic energies under the moment-curvature backbone curve at the ultimate curvature state and that at the MCE curvature state. Such scaling eliminates the need for conducting many NTHA for establishing partial collapse depicted by the failure of coupling beams.